Closing discussions can be used in situations where you want to conclude commenting on an existing thread that may now be out of date and you want to direct users to an updated thread or when simply closing a thread to comments altogether.
Who Can Close Discussions?
The ability to 'Close' discussions is a permission that should be restricted to a select few users like Administrators and sometimes Moderators. This would convert the discussion into a Read-Only state and no longer allow users to comment.
This permission is controlled by Roles and Permissions. A user would require the Close permission under Default Category Permissions or the Close permission for that particular category.
Please note that users who have the ability to close discussions also have the ability to comment on closed discussions.